A particle is moving with acceleration a ( t ) = 18 t + 16 . Its position at time t = 0 is s ( 0 ) = 10 and its velocity at time t = 0 is v ( 0 ) = 16 . What is its position at time t = 8 ?

Answers

Answer 1

Answer:

[tex]s(8)=2186[/tex]

Step-by-step explanation:

A particle is moving with acceleration modeled by the function:

[tex]a(t)=18t+16[/tex]

We are given that its position s(t) at t = 0 is 10 and that its velocity v(t) at t = 0 is 16.

And we want to find its position at t = 8.

Velocity is the integral of the acceleration. Hence:

[tex]\displaystyle v(t)=\int a(t)\, dt=\int 18t+16\, dt[/tex]

Find the velocity. Remember the constant of integration!

[tex]v(t)=9t^2+16t+C[/tex]

Since v(t) is 16 when t = 0:

[tex](16)=9(0)^2+16(0)+C\Rightarrow C=16[/tex]

Hence, our velocity is given by:

[tex]v(t)=9t^2+16t+16[/tex]

Position is the integral of the velocity. Hence:

[tex]\displaystyle s(t)=\int v(t)\, dt=\int 9t^2+16t+16\, dt[/tex]

Integrate:

[tex]\displaystyle s(t)=3t^3+8t^2+16t+C[/tex]

s(t) is 10 when t = 10. Hence:

[tex]C=10[/tex]

So, our position function is:

[tex]s(t)=3t^3+8t^2+16t+10[/tex]

The position at t = 8 will be:

[tex]s(8)=3(8)^3+8(8)^2+16(8)+10=2186[/tex]


Related Questions

Can someone help me with this question please.

Answers

The answer is 135 degrees.

Explanation:

tan(135) = -1

LHS: tan^2(135) = tan(135) x tan(135) = -1 x (-1) = 1
RHS: tan(135) = -1

LHS ≠ RHS

59:40
20-
What are the domain and range of the function on the
graph?

O The domain includes all integers
, and the range is y
0.
12+
O The domain includes all integers, and the range is
8-
The domain includes all real numbers, and the range
is y 2 0.
The domain includes all real numbers, and the range
is y > 0
4
1
2
3
4
5
6
7 X

Answers

Answer:

The domain includes all real numbers, and the range is y > 0.

Step-by-step explanation:

It is represented by [x] read as step 'x'

It is defined for all x

∴ domain=(−∞,∞)

The range is y > 0.

If 4 blocks weigh 28 ounces how many blocks weigh 70 ounces

Answers

Answer:

10 blocks.

Step-by-step explanation:

Find the unit rate.

[tex]\frac{28}{4}=\frac{7}{1}=\frac{70}{10}[/tex]

Therefore, 10 blocks weigh 70 ounces.

10 blocks just answering for points plz mark me brainiest

The axis of symmetry for the graph of the function f(x) = 2x2 + 3x + 10 is x=6. What is the value of b?
Ο Ο Ο Ο
3

Answers

Uhhhhh whatttt is it a question or a answer ?

What is the value for X?​

Answers

Answer:

5

Step-by-step explanation:

6x + 4 + 73 + 73 = 180

6x + 150 = 180

6x = 30

x = 5

Those little marks on AB and BC denote congruence. That makes the triangle isoceles. That means the base angles are equal. Both 73.

Triangle Sum Theory states all angles of a triangle add to 180.

y - (-9) = 8?

I am confused

Answers

Answer:

y = -1

Step-by-step explanation:

y - ( - 9) = 8

y + 9 = 8

y = 8 - 9

y = -1

- ( - turns to + because you are subtracting a negative number

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

-Chetan K

Answer:

y = -1

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to Right  

Equality Properties

Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of Equality

Step-by-step explanation:

Step 1: Define

Identify

y - (-9) = 8

Step 2: Solve for y

Simplify:                                                                                                             y + 9 = 8[Subtraction Property of Equality] Subtract 9 on both sides:                        y = -1

D'andre was trying to make a rectangular frame that had a width of 24 inches and a length of 70 inches. He wanted to ensure his shape contained right angles, so he measured the diagonal and found that it was 74 inches long. Did D'andre construct a rectangle? Why or why not?

Answers

Answer:

yes

the sum of the squares of the width and length is equal to the square of the diagonal

Step-by-step explanation:

The Pythagoras theorem : a² + b² = c²

where a = length

b = base

c =  hypotenuse

24^2 + 70^ = 576 + 4900 = 5476

square root = 74

What is GC?
I need help Please!

Answers

The correct answer is A

Sketch the graph of y = negative 2 x squared + x + 1 using your graphing calculator. What are the x-intercepts of this graph? a. (1, 0) and (-0.5, 0) c. There are no x-intercepts b. (-2.5, 0) and (-2, 0) d. (-1.5, 0) and (-0.5, 0) Please select the best answer from the choices provided A B C D

Answers

y= -2x²+ x + 1

i think it's A ?

Answer:

a

Step-by-step explanation:

eng. 2022

What number is equal to its opposite?

Answers

Answer:

zero

Step-by-step explanation:

HELPPP!!! ASAPPP!! PLEASE!! WILL GIVE EXTRA POINTS!!

Answers

Answer:

both of those lines intersect each other and are equal lines

Step-by-step explanation:

w²-10w-24

I really need help right now ​

Answers

Answer:

(w−12)(w+2)

Step-by-step explanation:

Step-by-step explanation:

w²-10w-24

(w²-12w)+(2w-24)

w(w-12)+2(w-12)

(w-12)(w+2)

What is 6x3-5+21/3?

Answers

Answer: 20

Step-by-step explanation:

First is 6 x 3 which is 18 then take away 5 so it would be 13 and + 21/3 is basically a seven so its 20

3. A bag contains 10 green and 5 grey marbles. If you pick a marble, record its color,
and return it to the bag 150 times, how many times can you expect to pick a gray
marble?
a. 15
b. 50
c. 750
d. 2,000

Answers

The answer is B.50
Because it’s Plato

What is the solution to the equation 6y –2(y + 1) = 3(y – 2) + 6?
y = –10
y = –2
y = 2
y = 6

Answers

Answer:

y = 2

Step-by-step explanation:

6y - 2(y + 1) = 3(y - 2) + 6

6y - 2y - 2 = 3y - 6 + 6

6y - 2y - 2 = 3y

4y - 2 = 3y

4y - 2 + 2 = 3y + 2

4y = 3y + 2

4y - 3y = 3y - 3y + 2

y = 2

The mean of ten numbers is 58. If one of the numbers is 40,
what is the mean of the other nine?

Answers

60

if the mean of ten numbers is 58 then the total would be 580 and when you subtract 40 from 580 you get 540 and then divide 540 by 9 for the new mean of 60

Organize from least to greatest

Answers

Answer:

y=31x/15 < y=27x/13 < y=15x/7 < y=13x/6 < y=11x/5 < y=21x/9 (=7x/3) < y=19x/8

Step-by-step explanation:

since all equations base on a linear, simple expression of x, we can simply compare the fractions.

in general, the bigger the number at the bottom, the smaller the individual fraction. that is our first indicator.

we then notice that many fractions represent the value of 2 plus one fraction.

31/15 = 2 1/15

27/13 = 2 1/13

15/7 = 2 1/7

13/6 = 2 1/6

11/5 = 2 1/5

the only exceptions are 21/9 and 19/8

but 21/9 is actually 7/3 = 2 1/3

and fits therefore into the list above.

that leaves 19/8 = 2 3/8.

the list above can be sorted based on the single fraction at the end (remember, the bigger the number at the bottom, the smaller the value). so, from least to greatest :

2 1/15 (31/15)

2 1/13 (27/13)

2 1/7 (15/7)

2 1/6 (13/6)

2 1/5 (11/5)

2 1/3 (7/3 = 21/9)

where did now 2 3/8 fit in ?

well, 3/8 is almost 1/2 (so, relatively big), and we start our comparison with the biggest number in the list so far :

1/3 (from 2 1/3).

what is bigger - 1/3 or 3/8 ?

let's find the smallest number that can be divided by 3 and by 8. that would be 24. so now we bring both fractions to the same base of 24.

1/3 = 8/24

3/8 = 9/24

=> 3/8 > 1/3

and therefore, 19/8 is the largest value and at the end of the list.

Suppose a normal distribution has a mean of 48 abd a standard deviation of 5. What is the probability that a data value is between 48 and 52?

Answers

Answer:

P(48<x<52) = 0.2881

Step-by-step explanation:

P(48<x<52) = normalcdf(lower,upper,µ,σ) = normalcdf(48,52,48,5) ≈ 0.2881

Therefore, the probability that a data value is between 48 and 52 is 0.2881, or about a 28.81% chance of occurrence.

3. sin t + cos2 t / sin t =

Answers

See the picture, please!!

Simplify. x 0 yz -3


Simplify. x 0 yz -3

Answers

Answer:

y / z^3

Step-by-step explanation:

x^0 is 1 because anything to the zero power is 1

1 *y z^-3

We know a^-b = 1/a^b

y / z^3

Answer:

[tex] \small \sf \frac{y}{z {}^{ 3}} [/tex]

Step-by-step explanation:

x⁰yz-³

Any non expression raised to power of 0 equals 1.

[tex] \small \sf \: 1yz {}^{ - 3} [/tex]

Express with positive exponents using [tex] \small \sf \: a {}^{ - n} = \frac{1}{a^n}[/tex]

1y +[tex] \small \sf \frac{1}{ z {}^{ 3}} [/tex]

[tex] \small \sf \frac{y}{z {}^{ 3} }[/tex]

how do i solve this in standard form ( see image)

Answers

Answer:

-25

Step-by-step explanation:

Let h = -3.

[tex](8(-3)-1)-(-3+3)\\(-24-1)-(-3+3)\\-25-0\\-25[/tex]

10. A model ship is 28 in. by 65 in. Use the scale 1 in.: ft to find the dimensions of the actual ship. 28 ft by 65 ft 14 ft by 32 325 Ft 84 ft by 195 ft 14 ft by 65 ft​

Answers

Answer:

14 by 32.5

Step-by-step explanation:

Which graph represents the function f(x) = -|x| -2

Answers

Answer:

my answer is in this picture

What are all the possible values of x? (This is not a right triangle!)

Answers

Answer:

2 < x < 5

Step-by-step explanation:

In a triangle a side must be major than the difference of the other two and minor of the sum of the other two

7-5 = 2

7+5 = 12

in the figure we can see that x is the smallest side

PLSS HELPP QHEJJEWJAKWK


What is the vertex of the parabola in the graph?

Answers

Answer:

(-3,-4)

Step-by-step explanation:

The vertex is the minimum or maximum or a parabola.

This is an upward opening parabola, so it has a minimum.

The minimum is (-3,-4)

Nandan bought some pencils at the rate of Rs 20 per pencil . He also bought an equal number of erasers at the rate of Rs 4 per eraser . He made 40 % profit on pencils and 50 % profit on erasers . At the end of the day, all the pencils and erasers were sold out and he made a profit of Rs 470 . Find the number of pencils he purchased.

Answers

Answer:

47 pencil

Step-by-step explanation:

Let x represent the number of pencils that were bought. Since equal number of erasers where also purchased, hence x erasers were purchased.

Cost of pencils = Rs 20 per pencil * x pencils = 20x

Cost of erasers = Rs 4 per eraser * x eraser = 4x

40% profit was made on pencils, hence:

Profit on pencils = 40% of cost price = 0.4 * 20x = 8x

50% profit was made on erasers, hence:

Profit on eraser = 50% of cost price = 0.5 * 4x = 2x

Since the total profit from pencil and eraser was Rs 470, hence:

8x + 2x = 470

10x = 470

x = 47

Therefore he purchased 47 pencil

the product of two integers is 96. One of them is-12, find the other numbers​

Answers

Answer:

-8

Step-by-step explanation:

let the other number be x

according to the question equation is

-12x = 96

x = 96/-12

x = -8

X=-8 djdnfhisnxvjhck

What’s the exponent ion regression equation for hat first these data.

Answers

the answer is in the picture

Which parent function is f(x) = |x|?

A. The quadratic parent function
B. The absolute value parent function
C. The linear parent function
D. An exponential parent function​

Answers

Answer:

it B

Step-by-step explanation:

xhdbsxjnysnkh rxdhwbejdxigj

What is the interest charge on $45.75 at 1.8% interest?
O $84.77
O $0.82
O $0.05
O $0.77

Answers

Answer:

.82

Step-by-step explanation:

45.75 x .018=.82

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